Cerebrovascular diseases, including stroke and dementia, rank among the top 10 causes of death globally. Where the Circle of Willis is an anatomical structure at the base of the brain that redistributes blood flow. Vrselja et al. challenged the traditional view that the primary function of the Circle of Willis is to provide collateral circulation, suggesting instead that it dissipates high pressures in the cerebrovasculature.

One-dimensional (1D) modeling, based on the simplified Navier-Stokes equations, offers a way to accurately predict blood flow with only a fraction of the computational expense of a three-dimensional (3D) model. SimVascular, a computational modeling software tailored for representing blood flow, recently added a 1D modeling feature. This study assessess the suitability of the 1D model in SimVascular for representing the cerebrovasculature, by testing it on the Circle of Willis. Additionally, preliminary research investigates whether the Circle of Willis functions as a pressure dissipative system, particularly through its communicating arteries.

The modeling pipeline included centerline extraction, mesh generation, boundary conditions, material model and solver parameters. Challenges were identified during centerline extraction, as SimVascular is inherently unable to handle loops, and inlet boundary conditions, where it could not manage multiple inlets. Considering these limitations, a series of 1D linear elastic models were created from the 3D geometry of the Circle of Willis to test whether it serves as a pressure dissipative system.

While SimVascular was unable to handle closed-loop geometries and multiple inlets, results indicated that the absence of a communicating artery induced relatively minor pressure oscillations. This suggests first, that SimVascular, in its current form, is not well-suited for 1D modeling of the cerebrovascular system's complexities, including loops and multiple inlets. Second, that the hypothesis of the Circle of Willis functioning primarily as a pressure dissipative system holds promise but requires further validation.

The study of haemodynamics, or the mechanics of blood flow, has been a topic of significant interest since ancient times, as it provides critical insights into both the normal functioning of the circulatory system and the mechanisms underlying various diseases. A robust scientific understanding of these dynamics facilitates the development of innovative prevention and intervention strategies, such as advanced, less invasive surgical techniques and cost-effective medical devices, which can dramatically improve global health outcomes. Over the centuries, experimental, analytical, and, more recently, computational methods have enhanced our knowledge of cardiovascular and cerebrovascular conditions, leading to improved diagnostic and therapeutic approaches that enhance life quality and expectancy.

Despite these advancements, substantial challenges remain, particularly in diagnosing and understanding haemodynamic complications such as stroke, stenosis, and regurgitation. Modern imaging techniques like MRI and sonography are limited by spatial and temporal resolution, requiring significant hardware improvements to overcome these constraints. Moreover, while analytical models have evolved to address the complex nature of blood flow and vessel behavior, they often struggle to accurately represent in vivo scenarios, especially in areas like the cerebral vasculature that are difficult to image. The presence of anomalies such as medial calcifications - which are responsible behind numerous life altering conditions and diseases such as, diabetes, kidney disease and hypertension - further complicates the accurate modeling of blood flow dynamics by introducing departure from axisymmetry, changes in material properties of the tissue and impacting the physics at localized scale.

To address the impact of medial calcifications, this thesis presents a detailed approach starting with the development of a three-dimensional (3D) model that represents the physiological fluid-structure interaction (FSI) phenomenon of pulsatile blood flow through an Internal Carotid Artery (ICA) with medial calcification. ICA is a critical vessel within the Circle of Willis which itself is one of the most crucial cerebro-vascular networks. Following this, a physics based one-dimensional (1D) Reduced Order Model (ROM) is developed, integrated with which is a data-driven constitutive modelling framework trained on the 3D simulation data, to account for changes in material proeprties introduced by medial calcifications. This ROM aims to provide a computationally efficient yet accurate representation of the physiological changes caused by medial calcifications. The thesis includes a comprehensive theoretical framework, detailed validation and verification processes, and comparisons between the 1D and 3D models to ensure accuracy and clinical relevance. The overarching goal is to create a well-validated ROM that maintains essential physical details while reducing computational costs, with an emphasis on evaluating its performance in clinical scenarios and exploring its potential applications and future research directions.

Trans-catheter aortic valve replacement (TAVR) has been widely used for treating Aortic stenosis (AoS). Numerical simulation of TAVR process is valuable in terms of reducing surgical risk for patients and cost for valve design. Finite element simulations are performed in this thesis to investigate the risk of coronary obstruction for patients who went through Aortic Valve Neo-cuspitization (AVNeo or Ozaki) procedure. The Expected Leaflet-to-ostium Distance was used as a criterion for assessing coronary obstruction risk. This value in 3 different deployment configurations is compared to determine the optimal deployment strategy. It is found that there is a large risk of coronary obstruction after TAVR for such patients under distal and midplane configuration but no risk under proximal configuration.

Ascending thoracic aortic aneurysm is a dangerous condition which is hard to locate in patients. CFD can be used to assess someone’s risk of suffering from such an aneurysm and also to assess any possible relation of an aneurysm with relevant parameters, like the shape of the aorta or how blood flows into the aorta.

Existing research on ascending aortic CFD flow generally focuses on assessing relatively high wall shear stress, seen as the cause for aortic wall damage and aneurysms, in patients and not much on any possible relationships between aortic shape and inflow with ascending aortic aneurysm. Work that does exist often uses 4D flow MRI, shown to produce results regarding peak wall shear stresses with less accuracy compared to CFD.

This thesis aims to supply that information using an aortic geometry from a large dataset of synthetically generated aortas together with synthetically generated inlet velocity profiles, showing a possibility to work with-out the need for patient measurements. The main work in this thesis focuses on finding any possible relationship between aortic inflow angle and relatively high wall shear stress, such that the results may better explain how aortic inflow can influence the appearance of aneurysms.

For this, a workflow has been established that allows working with large aortic geometry and inflow profile datasets with relative ease. This workflow process uses a mix of OpenFoam and Ansys Fluent usage.

Results have shown that the flow jet angle in the core of the flow has a significant negative correlation with peak WSS within the ascending aorta for the chosen aortic geometry. This is in contrast with other work showing positive correlations with WSS. This may suggest aortic geometry dependence together with the need to look at other flow variables, like jet impingement angle, to explain how aortic inflow can influence high WSS within the ascending aorta.

Recommendations for future work include: The same study but with a focus on aortas of healthy young people to see if aortas at risk can be found, as existing work mainly focuses on old people with ascending thoracic aortic aneurysm, a similar study with a focus on the inclusion of various aortic geometries to find how aortic geometry may influence the effect inflow variables can have on high WSS, the creation of a tool to easily calculate the impingement angle from aortic flow data and research into if aortic jet flow disruption could reduce peak WSS in the ascending aorta for use in aortic reconstruction.

Cardiovascular diseases (CVDs) are a group of disorders of the heart and blood vessels.
CVDs are the leading cause of death worldwide. To diagnose and treat CVDs, clinicians and cardiologists use multiple noninvasive imaging techniques. These scans are used to segment certain structures of the heart. Deep learning-based cardiac segmentation on short-axis cardiac magnetic resonance images (CMRI) has gained popularity over the past few years because of its generalisability and accuracy. This has exponentially reduced contouring times for clinicians. The development of such deep learning techniques has seen a common trend. In order to accommodate learning for larger cardiac datasets, the depth and size of segmentation networks have been increased. Unfortunately, the environmental impact of exploding such networks is not taken into account. One solution to mitigate having computationally expensive networks is to incorporate anatomical knowledge in the form of shape priors. The Gridnet and UNet with a shape prior are computationally efficient networks that are used to evaluate segmentation performance on a large and varied cardiac dataset (Combination of the Automated Cardiac Diagnosis Challenge - ACDC and Multi-Centre, Multi-Vendor and Multi-Disease Cardiac Segmentation challenge - M&M datasets). On average, these networks segment CMRIs with an average dice score of 0.87 and a Hausdorff distance of 11.7mm. In parallel, one of the major issues in cardiac technology is the under-representation of women in cardiac datasets. Purposefully curated cardiac datasets such as ACDC and M&M try and maintain equal representation. In real-world scenarios, this might not always be the case. Clinical trials to collect such data often report female representation as low as 25%. Evaluation of segmentation performance between a balanced and skewed dataset is conducted. This is to address if bias in such cardiac training datasets affects the performance of segmentation networks between male and female test patients.